Series question: find 0.01^0.01

Michael_Light · Feb 22, 2012

Homework Statement

By expressing x^x as a power of e and using the exponential series, or otherwise, find (without using tables) the value of x^x when x=0.01, correct to three places of decimals. (ln10 = 2.30 to two decimal places).

Homework Equations

The Attempt at a Solution

I have tried to playing around with the exponential series and ln 10 = 2.3, but still can't get anything useful... can someone guide me?

Handwritten working: the series e^x = 1+x+x^2/2!+x^3/3!+..., then e^(x·x) = 1+x·x+(x·x)^2/2!+(x·x)^3/3!+..., then ln 10 = 2.3, ln 0.01 = -4.6, and 0.01 = e^(-4.6).

tiny-tim · Feb 22, 2012

Hi Michael!

Michael_Light said:

By expressing x^x as a power of e

But you haven't done that …

you've written e^{x^x} …

you're being asked to find y, where e^y = x^x

Series question: find 0.01^0.01

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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